Types of Data

Statistics is the branch of Mathematics that deals with collecting, organizing, presenting, and interpreting data. Before you can draw a graph or calculate an average, you must first understand the type of data you are working with.

In CSEC Mathematics, questions often ask you to classify data as qualitative or quantitative, and to decide whether numerical data is discrete or continuous. You may also need to know the difference between ungrouped data and grouped data.

What you will learn

• Understand what data means in statistics
• Tell the difference between qualitative and quantitative data
• Tell the difference between discrete and continuous variables
• Recognise ungrouped and grouped data
• Classify different types of data in exam-style questions

Key Ideas

What is Data?

Data means information that has been collected. This information can be collected from surveys, tests, measurements, observations, or records.

For example, a teacher may collect data about:

• Students' test scores
• Students' favourite subjects
• The height of each student
• The number of students absent each day
• The time taken by students to complete a race

Not all data is the same. Some data uses words or categories, while other data uses numbers.

Qualitative Data

Qualitative data describes a quality, name, label, category, or characteristic. It is usually not numerical.

Examples of qualitative data include:

• Favourite colour
• Type of vehicle
• Favourite sport
• Gender
• Nationality
• Brand of phone

Qualitative data answers questions such as What type?, Which category?, or What kind?

Question	Possible Answers	Type of Data
What is your favourite colour?	Blue, red, green	Qualitative
What sport do you play?	Football, cricket, netball	Qualitative
What brand of phone do you use?	Samsung, Apple, Tecno	Qualitative

Quantitative Data

Quantitative data is data that is numerical. It involves numbers that can be counted or measured.

Examples of quantitative data include:

• Number of children in a family
• Number of goals scored in a match
• Height of a student
• Mass of a bag
• Time taken to run 100 m
• Marks scored on a test

Quantitative data answers questions such as How many?, How much?, How long?, or How heavy?

Question	Possible Answers	Type of Data
How many goals were scored?	0, 1, 2, 3	Quantitative
What is your height?	156 cm, 162.5 cm	Quantitative
How long did the race take?	12.4 seconds	Quantitative

Qualitative vs Quantitative Data

Type of Data	Meaning	Examples
Qualitative	Describes qualities or categories	Colour, sport, type of car
Quantitative	Uses numbers	Age, height, number of goals

Variables

A variable is something that can change or take different values.

For example:

• The number of students in a class can change.
• The height of a student can vary from student to student.
• The time taken to complete a race can be different for each person.

Quantitative variables can be classified as discrete or continuous.

Discrete Variables

A discrete variable can only take separate, countable values. These are usually whole numbers.

Discrete data is counted, not measured.

Examples of discrete variables include:

• Number of children in a family
• Number of cars passing a school
• Number of goals scored in a match
• Number of students in a classroom
• Number of books on a shelf

You cannot have half a student, half a car, or half a goal in these situations. That is why the values are separate and countable.

Example 1: Classify “the number of cars passing a school each hour”.

1. This is numerical because it is a count.
2. It is quantitative data.
3. You can count 10 cars, 11 cars, or 12 cars.
4. You cannot count 10.5 cars.
5. Therefore, the values are separate and countable.
6. Answer: Discrete quantitative data

Continuous Variables

A continuous variable can take any value within a range. Continuous data is usually measured.

Examples of continuous variables include:

• Height
• Mass
• Time
• Temperature
• Length
• Speed

Continuous data can include decimals. For example, a student’s height could be 160 cm, 160.5 cm, or 160.53 cm, depending on how accurately it is measured.

Example 2: Classify “the mass of each student in kilograms”.

1. Mass is numerical, so it is quantitative data.
2. Mass is measured, not counted.
3. A student could have a mass of 45 kg, 45.5 kg, or 45.75 kg.
4. Since mass can take many values within a range, it is continuous.
5. Answer: Continuous quantitative data

Discrete vs Continuous Variables

Type of Vari­able	Meaning	Usually Found By	Examples
Discrete	Separate, count­able values	Counting	Number of students, goals, cars
Contin­uous	Any value within a range	Measur­ing	Height, mass, time, temper­ature

Ungrouped Data

Ungrouped data lists the individual values exactly as they are collected.

For example, the marks scored by 10 students are:

This is ungrouped data because each value is shown separately.

Ungrouped data is useful when the data set is small and easy to read.

Grouped Data

Grouped data puts values into groups or class intervals. This is useful when there are many values.

For example, instead of listing every test mark separately, the marks can be grouped like this:

Mark Interval	Frequency
0 - 9	2
10 - 19	5
20 - 29	8
30 - 39	4

This is grouped data because the individual values are placed into intervals.

Ungrouped vs Grouped Data

Type of Data	Meaning	Example
Ungrouped data	Values are listed individually	4, 5, 6, 6, 7, 8
Grouped data	Values are placed into intervals or classes	0 - 9, 10 - 19, 20 - 29

Worked Examples

Example 3: State whether “favourite colour” is qualitative or quantitative.

1. Favourite colour is not a number.
2. Possible answers include blue, red, green, and yellow.
3. These are categories or qualities.
4. Answer: Qualitative data

Example 4: Is “the time taken to run 100 m” discrete or continuous?

1. Time is numerical, so it is quantitative data.
2. Time is measured, not counted.
3. It can include decimals, such as 12.4 seconds or 12.43 seconds.
4. Answer: Continuous

Example 5: Is “the number of goals scored in a match” discrete or continuous?

1. The number of goals is counted.
2. You can score 0, 1, 2, or 3 goals.
3. You cannot score 2.5 goals in a match.
4. Answer: Discrete

Common Mistakes

• Thinking all numbers are continuous. Some numbers are counts, so they are discrete.
• Calling a category quantitative just because it has many possible answers.
• Forgetting that continuous data is usually measured and can include decimals.
• Confusing grouped data with ungrouped data.
• Forgetting that grouped data uses class intervals.

Exam-style multiple choice

Practice Questions

1. Is “the number of goals scored in a match” discrete or continuous?
2. Is “the time taken to run 100 m” discrete or continuous?
3. State whether “favourite colour” is qualitative or quantitative.
4. State whether “height of students” is qualitative or quantitative.
5. State whether “number of students in a class” is discrete or continuous.
6. State whether “temperature of a room” is discrete or continuous.
7. Give two examples of qualitative data.
8. Give two examples of quantitative data.
9. Explain the difference between ungrouped and grouped data.
10. Classify “the number of messages received in one day” as discrete or continuous.

Answers

1. Discrete
2. Continuous
3. Qualitative
4. Quantitative
5. Discrete
6. Continuous
7. Examples: favourite colour, type of car, favourite sport, brand of phone
8. Examples: height, mass, age, number of students, test score
9. Ungrouped data lists each value separately, while grouped data places values into class intervals.
10. Discrete